未得獎作品

任意一個三角形要如何分割成四個彼此相似的組成三角形呢？我們透過嚴謹的數學推理，先對三角形作二、三分割的可能情形進行驗證，並藉由已完成相似二、三分割的三角形，運用「內分」和「外加」的觀念，使相似四分割的討論變得明快，並得以將各式三角形的所有相似四分割的圖示作完整而有系統的呈現。 \r 我們也對「比例四分割」的作圖法與其相關幾何性質，進行猜想與討論，並驗證得出一些結果。尤其對「黃金三角形」經比例四分割後，組成三角形之對應邊長的比值也是「黃金值」，以及使用五條摺痕線的摺紙方式，可以摺出一張黃金三角形紙張的比例四分割，這些研究結果都令我們感到獲益良多。 How to divide a triangle into four similar little triangles？ Possible situations of dividing a triangle into two or three parts could be testified by strict mathematical inferences, and then the concepts of “internal division” and “external addition” could be applied to make our discussion clearly and briefly. With above discussions, figures about four similar divisions of all kinds of triangles could be presented completely and systematically. Some results were come up after making some conjectures and discussions about the geometric constructions and geometric properties of “four proportional divisions”. We learn a lot by these researches especially on the discoveries that the ratio of those corresponding sides in each four similar triangles which form a golden triangle, is also golden ratio; and that we could divide a golden triangle into four similar triangles by using five folding lines.

A novel and simple method was developed to determine the activity of silver in nanometer particles more than in non-nanometer particles. The conductivity of conducting polymer, polyaniline (PANI) doped with different amount of nanometer silver particles was used to evaluated the activity of nanometer silver. In polymerization of polyaniline, hydrogen chloride solution usually used to increase the conductivity of polyaniline. When 1%(w/w) nanometer silver particles doped during the polymerization, the conductivity of polyaniline was down from 2.28 s/cm to 0.65 s/cm, then increased with increasing the amount of nanometer silver doped. The conductivity of polyaniline was changed from 2.28 s/cm to 0.47 s/cm when 3%(w/w) nanometer silver particles doped, but it is increased from 2.28 s/cm to 2.44 s/cm when was doped with 3%(w/w) micrometer silver particles. The conductivity of polyaniline changed due to the formation of silver chloride (AgCl) in doping nanometer silver. Some of the nanometer silver particles were formed to silver ion in hydrogen chloride solution for the high activity property of nanometer silver. This also can be proved from the spectra of XRD and FE-SEM. Therefore; determination the conductivity of conducting polymer by doping nanometer metal particles can be used to determine the activity of the nanometer particles. 本研究為開發一個新穎的檢測奈米金屬粒子化學活性大於非奈米金屬粒子的簡易方法。方法為利用導電高分子聚苯胺，於合成過程中添加不同濃度的奈米銀粒 子，並分別偵測其成品的導電度，藉以評估奈米銀粒子的化學活性。由於聚苯胺在合成過程中通常加入鹽酸以提高其導電度，致活性較大的奈米銀粒子於氧化後，隨即與氯離子形成氯化銀的沉澱，而降低聚苯胺的導電度，如添加1﹪(w/w)奈米銀粒子的，其導電度由2.28 s/cm 降至0.65 s/cm，隨後隨著添加量的增加導電度先降後再稍回升。一般非奈米級銀粒子因氧化電位為負值，即化學活性小，而不易被氧化。由實驗結果，我們發現同樣添加3%(w/w)的奈米級銀粒子或微米級銀粒子，添加奈米級銀粒子的導電度由2.28 下降為0.47，添加微米級銀粒子的導電度卻由2.28 上升為2.44，此乃說明本方法確實足以證明奈米級金屬的化學活性的確遠大於微米級金屬，因相同條件下，微米級銀粒子未如同奈米級銀粒子一樣被氧化成銀離子。即奈米級銀粒子可以輕易的被氧化，而非奈米級銀粒子則不易被氧化。尤其也可由X 光繞射儀分析光譜圖和場發射式掃描電子顯微鏡拍攝圖證明。因此，我們可以採用添加3 %(w/w)奈米級金屬銀粒子及微米級金屬銀粒子於導電高分子的方法，並藉導電度的變化，證明奈米金屬粒子的高活潑性。

在台灣公共場合快速成長下，例如：大賣場、百貨公司、展覽會場，這些公共大型場合都有很好的消防設施，但始終有人葬身於火場？ 原因就是幾乎所有的人都不會去特別注意逃生平面圖，導致花太多的時間尋找出口，這樣生存機率就大大降低。火場裡面有太多的致命因素，像是：高溫的空氣，毒氣、濃煙…等，所以必須把握每一分每一秒。為了加快逃生速度，我們將所有的通道都設有導引警示器，逃生者只要順著導引警示器就可以安全到達出口。為了因應公共場合有龐大的人群，所以逃生路線不能只有一條，因此我們設計上是有多條路線，一、可以解決龐大人群，二、可以加快速度。;With the rapid growth of public places in Taiwan, evacuation system is of more and more importance. Actually, public places, such as hyper malls, department stores and exhibitions, are not without fire-fighting equipment, but why is that there are still people getting killed in a fire? The reason is that almost no one actually pays attention to the evacuation plans. As a result, it often takes too much time to find the exits, which lowers the possibility of survival. In a fire, there are usually too many fatal factors, which could lead to death, such as high temperature and heavy smoke; therefore time is precious when escaping from a fire. To fasten the speed of evacuation, we set guiding alarms in every passageway. By following the guiding alarms, people can get to the exits safely. Besides, owing to the huge amount of population in public places, there can’t be only one route out. With regard to this, we design many routes in order to enable and fasten the speed of evacuation of huge amount of population.

在本次的實驗中，我們藉由拉午耳定律的公式及一條由作者從實驗中推論而得的公式，可以簡單的求出不同溶液的分壓。我們只需要一個自製式的簡易裝置，在裝置底下放置被測量的溶液，並密封使其成為封閉系統，其頂端為一銅箔，在銅箔上使用適合的溶液，藉由上方溶液蒸發量與下方不要放置溶液蒸發量的差異之值比較，即可求出其下方兩種成份系的溶液中各種溶液在不同莫耳分率下的分壓以及能量的傳遞，雖然會有誤差的存在，但比照一般利用光譜法來測量的方式，成本卻降低很多，且經由公式，也可估計各點的活性係數，比之以往簡易很多，因此可當作針對的高中生示範教學及教具，使同學更能了解兩成分係非理想溶液在拉午耳定律中之差別。This study shows that is easy to figure out the partial pressure of the different solutions by applying the formula of the Raoult's laws and a formula computed by the authors from their experiment data. All that is needed is a simple hand-made device. In the experiment, the device was sealed into a closed system after the solution to be measure was placed at the bottom of the device. A proper liquid was put in the top piece of the device, which was made of copper foil. By computing the difference between the amounts of evaporation of the top liquid with and without the bottom solution, we figured out that the two-component solution is the partial pressure and energy transmission of the solutions at varied mole fractions. Though errors do exist, cost was much lower by this method than by the spectrum method. Besides, the formula makes it easier to estimate the activity coefficients at different points. Therefore, the study can be applied in physics teaching in senior high school to facilitate students' understanding of the differences between two-component solutions in the Raoult's laws.

自2004年4月29日至2004年8月30日止，研究不同食物量對於蓋斑鬥魚生殖表現之影響。自臺北縣水產種苗繁殖場取得40尾（北縣種苗場字第0930000192號），分成低、中、次高、與最高四個飼養食物量組（3, 6, 9 ,12 顆飼料/每隻魚），每一種食物量組進行四次重複實驗，每一個實驗箱飼養雌、雄魚一對，控制相同的光週期、溫度、密度等變因。結果顯示食物量為中食量組（6粒/隻）泡巢維持時間最長，與其他三組統計上有顯著差異，而其他生殖表現如雄魚的吐泡巢次數、泡巢間隔時間，以及雌魚產卵次數、產卵間隔時間，和魚卵孵化時間等四組之間皆無明顯差異。因此推測不同飼養食物量的處理對於蓋斑鬥魚生殖行為之影響不顯著。From April 29, 2004 to August 30, 2004, we studied the effects on breeding behavior of Macropodus opercularis in different quantities of food. We got forty fish from the nursery in Taipei County. We breed one male and one female in the tank, and the quantities food was set to low, middle, high, and highest groups (3, 6, 9, 12 granule forage per one fish). Every experiment group repeated three times. We also controlled the same light cycle, temperature, and density. We found that the longest maintenance time per one foam nest was breeding in middle group, and there is a statistically significant difference. But the other results had no statistically significant differences between different groups. Therefore, we inferred that the different allowance food feeding control had no significant effect to breeding behaviors of Macropodus opercularis.

由於想了解化學反應的微觀形態，我們設計微型化學反應裝置來比較巨觀(傳統型)與微觀(創新型)化學反應間的差異，並探討其實用及環保方面的問題。在顯微鏡底下，我們觀察化學反應的沉澱結晶及電解反應，嘗試以各項變因(溫度、濃度、聲波…等)來觀察其結晶的型態。我們已成功地將實驗藥品用量減少到一滴(約0.04ml)，並以微觀的角度觀察化學反應的過程。在實驗中，發現反應進行時，粒子會不斷流動，經查證後為愛因斯坦所提出的布朗運動，並且測得硫顆粒的直徑大小約4.2 ~ 6.7 微米。不同聲波所造成硫粒子的移動速率不同，而不同溫度的部份，我們發現→每增加十度硫粒子移動速率增加約兩倍。在面積4.392×10-4cm2 範圍內大約有250~300 顆硫沉澱的粒子。本實驗成功地將顯微鏡應用在化學領域上，若將此實驗推廣，可達到污染少、觀察實驗的時間短、用量少的目標。此實驗是邁向化學微觀世界，一種值得嘗試且創新的方法。In order to compare the differences between the chemical reactions of macroscopic reactor and microscopic reactor, we have designed a device of chemical reaction and researched into the problems of their environmental protections and practical aspects. Under the microscope, we observed not only their precipitating crystal compound from the chemical reaction and electrolytic reation but their types of crystal. We have successfully reduced the dose to one drop ( about 0.04ml) and observed the process of their chemical reaction from the angle of microscopic reactor. During performing the experiment, we found the particles would keep flowing while the reaction was working. It was proved as "Brown motion" introduced by Einstein. The diameter of these particles were around 4.2~6.7μm. We find that different sound waves and temperatures,the motion speeds are quite different. And the movement rate increases about two times as the sulfer particles increase 10℃ each time .Within the measure of area of 4.392×10-4cm2,there are 250~300 sulfer particles.The experiment has successfully used a microscope in the field of chemistry. If we popularize the experiment, we can reach the goal of less pollution, fewer the dose and time-saving observation. It’s an innovation to step to the world of chemical microscope world.

本研究主題主要是解決化學上複雜同分異構物的繪製以及其命名，因為物質在結構複雜時其同分異構物變化之多令人難以捉摸，於是我應用電腦強大的邏輯處理以及運算判斷的能力來讓電腦繪製。以下是我想達成的目的：(1)排列出分子式的同分異構物(2)顯示出同分異構物之示性式、結構式(3)預知尚未創造出物質的性質研究中我創造出以下原則讓我方便達成研究(1) 數位密碼：為了讓電腦方便執行我使用數碼的方式表達各種同分異構物(2) 五大原則：此原則能讓不僅是電腦甚至是各個要繪製同分異構物的人都能有架構的繪製，不會遺漏任何的組成。(3) ３Ｄ顯示：透過Ｘ３Ｄ軟體的協助我能讓使用者透過立體的方式了解到物質的結構。The purpose of this research is to solve the problem of Isomer’s structure drawing and named problem. It’s hard to predict the status of complex Isomers, so we use the powerful logic and calculational ability of computer to draw the structure of Isomers. The following points is the goal that we want to reach (1) Arrange the structure of the Isomer’s formula (2) Show structural formula of Isomers (3) Predict the chemistry of things that haven’t been created During our research, we create the following principle to help us do the research (1) Digital Codes: In order to let the computer to run the process, we use digital codes to express all the Isomer’s formula. (2) The “5 Rules”: The 5 rules can help not only computers but all the people who try to draw the structure of Isomers without losing any of compositions. (3) 3D Display: Helping our user to understand the structures of materials with the 3D images producing by the “X3D”.

在實驗用共振法測量聲音在固體、液體、氣體中的駐波聲場，測量各介質中的聲速。研究超聲波在液體中的空腔效應，鋁箔在不同液體受空腔效應所破損面積與時間略成正比，並發現在水與各濃度的洗潔精水溶液中以水的破損效果最明顯。另外利用1.65MHz 高頻超聲波打入水中，因駐波使水有疏密不同產生狹縫，以雷射通過狹縫有光的繞射花紋產生，由干涉條紋可推估駐波波長。利用閃頻共振法研究光彈材料超聲波場，且發展出以肉眼觀測的裝置，由光彈材料的花紋級數與應力研究中，發現花紋級數與應力成正相關，由聲場中的花紋顏色判斷所受應力大小，並發現超聲波不僅有聲場產生並伴隨熱效應，會影響觀測花紋級數。This project began by studying the fundamental properties of acoustic waves, the relationship between its velocity, frequency and wavelength. Experiments regarding the distribution of sound waves in different mediums, and the induction of resonance in solid, liquid and gaseous materials were conducted. Results from utilizing suspending method to confirm theoretical prediction of sound velocity was accurate, and the sound wave patterns in photo-elastic materials were observed. It was also observed that an aluminum foil would be cut in an ultrasonic cleaning device. The effects of different liquids such as water and detergents on cleaning effectiveness were then experimentally determined, taking into account factors such as viscosity. From reference materials, we learned that ultrasonic waves would create Caritation in liquids. Traditionally, sound waves are expected to exhibit only longitudinal waves, yet in this study it was discovered that the residual\r stresses from resonance in photo-elastic materials also indicate the existence of transverse waves.

Chemistry experiments in school produce an abundance of waste in both materials and equipment. Since hands-on experimentation is a critical pedagogical tool the trend in classroom experimentation is clearly towards environmentally friendly experiments that scale, but was also able to measure reaction rate in blue cupric sulfate solution using the color dissipation as a rate gauge. There was an evolution of apparatus and experiment design beginning with simple magnifying glass optics and advancing to a custom made, light-gathering microscope video apparatus that allows the experiment to be monitored and files recorded for later viewing. I was inspired by the Yin Yang Sea phenomenon in Taipei County. The Yin Yang Sea is a coastal area in Chinkuashih, Taipei County where coastal currents in the area lack the strength to disperse the heavy metal pollutants that empty into the Lientung Bay. The result is a contrast between the blue sea water and the turgid yellow ground water. This contrast led me to add an all-purpose indicator to the reactant solution. This deepens the visual effect of the electrolysis experiment. 我們從環境保護的角度去思考學校的化學實驗時，減量減廢的微型化學實驗已是未來實驗的趨勢。經過多年的努力，我除了成功的做到電解最微量的一滴溶液外，對於從藍色硫酸銅溶液顏色消失的電解時間裡，還可做定量的檢定感到不可思議！為了更清楚看到液滴溶液的電解反應，儀器的設計由放大鏡到自組顯微投影機，最後進階到顯微視訊的畫面，它不但可記錄下來，而且可在電腦中播放。為了更清楚看到液滴溶液的氧化還原反應和酸鹼變化，我想到了在北台灣的金瓜石海域一處特別的景觀，那就是離岸近海處有黃藍兩個不同顏色的陰陽海！於是我加了廣用指示劑到液滴中，由電解後出現的的陰陽海畫面，更可加深實驗的效果。 最重要的是：最環保也最接近零污染的顯微化學實驗，已然是未來可發展下去的目標。

單淘汰賽是一種失敗一次即遭淘汰的賽制；在此假定每位選手都有一相對應的能力數值，本文主要探討在均高的單淘汰賽程表之下，若賽程安排完全依照種子安排原則(亦即最強的選手對最弱的選手、次強隊次弱….)，則對於能力越強的選手越有保障，直觀上而言能力最強的選手應有最大的奪冠機率，探討此種賽程安排是否滿足能力較強的選手有較大的勝率？因發現在某些特殊的選手能力數值分佈之下會發生次強選手勝率大於最強選手的情況，令A、B代表最強與次強選手，P(A)、P(B)代表A、B奪冠的機率，故擬定P(B)/ P(A)為參考依據，尋求P(B)/ P(A)的最大值發生處作為最極端的狀況。發現四位選手的情況下，P(B) / P(A)最大值 = 1；八位選手的情況下，P(B) / P(A)最大值=(196+98) / 343=1.0938，當選手數為2n時，P(B)/ P(A)最大值隨n的增加而遞增。 Knockout Tournament is a highly competitive system in which any player losing a game can no longer play in the tournament. Here we suppose that every player has a numerical value that corresponds to his ability. We consider a totally-seeded knockout tournament with 2n players where in the first round, the strongest player matches the weakest player, the second strongest player matches the second weakest player, and so on. We examine whether a stronger player always has a greater probability of winning the tournament. The answer is in the affirmative for n = 2. For a tournament with eight players(n = 3), the situation is much more complicated. In certain cases, the second strongest player has the greatest probability of winning the tournament. Specifically, let A and B denote the strongest and second strongest players, P(A) and P(B) their respective probability of winning the tournament. We find that the maximum value of P(B)/P(A)equals (196+98) / 343 = 1.0938. For n > 3, we have not obtained the maximum value of P(B) / P(A) . However, it can be readily seen that the maximum value of P(B) / P(A) is non-decreasing as n increases.